The most basic kind of inference about a population is an estimate of the location (or shape) of a distribution. The central limit theorem says that the sample mean is an unbiased estimator of the population mean and can be used to make a single point inference of the population mean. While making this kind of inference will give you the correct estimate on average, it seldom gives you exactly the correct estimate. As an alternative, statisticians have found out how to estimate an interval that almost certainly contains the population mean. In the next few pages, you will learn how to make three different inferences about a population from a sample. You will learn how to make interval estimates of the mean, the proportion of members with a certain characteristic, and the variance. Each of these procedures follows the same outline, yet each uses a different sampling distribution to link the sample you have chosen with the population you are trying to learn about.
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